document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160809>Question 160809</A>: <I><SPAN STYLE=\"word-break: break-all;\"> since the beginning of the month, a local reservoir has been losing water in a linear fashion. On the 12th of the month the resrviour held 200 million gallons of water, and on the 21st of the month it held only 164 million gallons. Assuming this continues, express the number of gallons as a function of time,t, where t is the number of days elapsed since the beginning of the month. Determine when the tank will be empty.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118559 by </B><A HREF=/tutors/aboutme.mpl?userid=AksharTech><B>AksharTech(1)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AksharTech><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.akshartech.com/favicon.ico valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=118559\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the reservoir has been losing water in a LINEAR fashion, the expresion of the function will be similar to the equation of a straight line.<BR>\n" );
document.write( "Standard equation of a straight line is as follows:<BR>\n" );
document.write( "y = mx + C\r<BR>\n" );
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document.write( "Replace y by the quantity of water and x by the time elapsed i.e. 't'.<BR>\n" );
document.write( "quantity of water = mt + C   ......(eq-1)\r<BR>\n" );
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document.write( "You get two equations by plugging the values provided in the question for Quantity of water and time elapsed.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200=m%2A12%2BC ALIGN=MIDDLE  ALT=\"200=m%2A12%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=164=m%2A21%2BC ALIGN=MIDDLE  ALT=\"164=m%2A21%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve this pair of linear equations.<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear.solver>Linear System solver (using determinant)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++12%5Cm+%2B+1%5CC+=+200%2C%0D%0A++++21%5Cm+%2B+1%5CC+=+164+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++12%5Cm+%2B+1%5CC+=+200%2C%0D%0A++++21%5Cm+%2B+1%5CC+=+164+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2Am+%2B+a%5B12%5D%2AC+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Am+%2B+a%5B22%5D%2AC+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++m+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++C+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++++m+=+%28200%2A1+-+164%2A1%29%2F%2812%2A1-21%2A1%29+=+-4%2C%0D%0A++++++C+=+%2812%2A164+-+21%2A200%29%2F%2812%2A1-21%2A1%29+=+248%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (m=-4, C=248}<BR>\n" );
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document.write( "You get m = -4 and C = 248<BR>\n" );
document.write( "Plug-in these values in eq-1 shown above. So you get the number of gallons as a function of time,t.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QuantityOfWater+=+-4%2At+%2B+248 ALIGN=MIDDLE  ALT=\"QuantityOfWater+=+-4%2At+%2B+248\"   DISABLED_style= \"max-width:90%; height:auto;\" >   ..... (Answer#1)\r<BR>\n" );
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document.write( "Plug-in 0 for the quantity of water in this equation to determine when the tank will be empty.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-4%2At%2B248 ALIGN=MIDDLE  ALT=\"0=-4%2At%2B248\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2At=248 ALIGN=MIDDLE  ALT=\"4%2At=248\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=248%2F4 ALIGN=MIDDLE  ALT=\"t=248%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=62 ALIGN=MIDDLE  ALT=\"t=62\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore the tank will be empty after 62 days. ....(Answer#2)\r<BR>\n" );
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